Solve for $$ x: \frac{11 x}{3 x+8}=1 $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\frac{11x}{3x + 8} = 1
$$

**Step 1: Eliminate the Denominator**

Multiply both sides of the equation by the denominator $$ 3x + 8 $$ to eliminate the fraction:

$$
\frac{11x}{3x + 8} \times (3x + 8) = 1 \times (3x + 8)
$$

Simplifying both sides:

$$
11x = 3x + 8
$$

**Step 2: Collect Like Terms**

Subtract $$ 3x $$ from both sides to gather the $$ x $$-terms on one side:

$$
11x - 3x = 8
$$

$$
8x = 8
$$

**Step 3: Solve for $$ x $$**

Divide both sides by 8 to isolate $$ x $$:

$$
x = \frac{8}{8} = 1
$$

**Step 4: Verify the Solution**

It's good practice to check if the solution satisfies the original equation and doesn't make the denominator zero.

Substitute $$ x = 1 $$ back into the denominator:

$$
3x + 8 = 3(1) + 8 = 11 \neq 0
$$

Since the denominator is not zero, $$ x = 1 $$ is a valid solution.

**Answer:**

$$
x = 1
$$
$$ x = 1 $$

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